Monthly Archives: September 2008

Decimal expansion zoo

In a comment on a previous post about rational numbers and decimal expansions, Steve Gilberg noted: I’ve been fascinated at how any multiple of 1/7 that’s not an integer repeats the same digits in decimal expression, only starting at different … Continue reading

Posted in number theory, pattern | Tagged , , | 14 Comments

Two Very Large primes

As promised, I can now reveal the identity of the two newly discovered Mersenne primes. The smaller of the two, discovered on September 6 by Hans-Michael Elvenich in Langenfeld, Germany, is an 11,185,272-digit number which you can download here. The … Continue reading

Posted in computation, famous numbers, links, primes | Tagged , , , | 3 Comments

New Mersenne primes!

The Great Internet Mersenne Prime Search just announced not one, but two new Mersenne primes! You might also recall the last time they announced a new prime, in September 2006, so these new primes were found almost exactly two years … Continue reading

Posted in computation, famous numbers, links, primes | Tagged , , , , | 1 Comment

Teaching precalculus in 2008-2009

This year I will be teaching precalculus via correspondence to two homeschool students. Don’t ask how this happened, it’s a long story, but I’m excited! It will be fun for me to gain more experience teaching and writing, and to … Continue reading

Posted in links, meta, teaching | Tagged , , , , | 6 Comments

Rational numbers and decimal expansions

As you may remember from school, rational numbers have a terminating or eventually repeating (periodic) decimal expansion, whereas irrational numbers don’t. So, for example, 0.123123123123…, with 123 repeating forever, is rational (in fact, it is equal to 41/333), whereas something … Continue reading

Posted in infinity, iteration, number theory, pattern | Tagged , , | 9 Comments

Weird black bars in LaTeX images

Recently I’ve been seeing strange black bars to the right of all the images generated from LaTeX expressions on this blog. But I’m starting to suspect that it’s some sort of bug in Firefox, because when I download the images … Continue reading

Posted in meta | Tagged , , , , | 22 Comments

Mandelbrot Maps

Run, don’t walk, to play with the Mandelbrot Maps applet, which lets you play around with the Mandelbrot set while seeing the associated Julia sets updated in real time. This fantastic applet was created by Iain Parris, an MSc student … Continue reading

Posted in fractals, links | Tagged , , , , ,